How to show $\sin(-iy)=i\sinh(y)$?use Euler's identity $ sin(x)= \frac{e^{ix}-e^{-ix}}{2i} $ and the definition of the hyperbolic sine $ sin(x)= \frac{e^{x}-e^{-x}}{2} $ now just compare :) since $ i(-i)=1 $